臺灣博碩士論文加值系統

摘要
針對具有彈性拘束(elastically restraint)的對稱斷面( symmetric cross-section )的預扭非均勻樑，基於Bernoulli-Euler樑的理論，及應用漢米爾頓( Hamilton )原理，進行預扭樑平衡方程式的推導，進而得到其統御方程式及其所對應的邊界條件。
運用轉換矩陣法( transfer matrix method )將所得到的統御方程式求出其確切解，進一步利用邊界條件來求得頻率方程式以得到整個預扭非均勻Bernoulli-Euler樑的自然頻率。
我們用本法所得到的結果和其他文獻裡得到的結果作比較，並且討論預扭角及錐度比對於各種不同次的自然頻率所造成的影響。

ABSTRACT
Based on the Bernoulli-Euler beam theory，the coupled governing differential equations with general eleastic boundary conditions for coupled bending-bending vibration of a elastically restrained and pretwisted nonuniform beam of rectangular cross-section are derived by using Hamilton’s principle.
The transfer matrix method is presented to study the vibrations of any pretwisted nonuniform beam of rectangular cross-section. The frequency equation is derived and expressed in terms of the transfer matrix. The corresponding results are compared with previous work in the literature. Finally，the influence of pretwisted angle and taper ratio on the natural frequencies is investigated.

目 錄
中文摘要…………………………………………………..Ⅰ
英文摘要…………………………………………………..Ⅱ
誌謝………………………………………………………..Ⅲ
目錄………………………………………………………..Ⅳ
圖目錄……………………………………………………..Ⅵ
表目錄……………………………………………………..Ⅶ
符號說明…………………………………………………..Ⅷ
第一章 緒論……………………………………………..1
1.1 前言……………………………………………………..1
1.2 文獻回顧……………………………………………….2
1.3 研究目的及方向………………………………………6
第二章 推導統御方程式及邊界條件………………….7
第三章 無因次化……………………………………….12
第四章 轉換矩陣法求解………………………………14
4.1 閉合型的場轉換矩陣……………………………….14
4.2 點轉換矩陣…………………………………………..18
4.3 頻率方程式…………………………………………..21
第五章 數值結果與討論……………………………..23
5.1 數值參數……………………………………………..23
5.2 數值比較……………………………………………..24
5.3 數值結果……………………………………………..25
第六章 結論…………………………………………….31
參考文獻…………………………………………………..34
附錄…………………………………………………….….38
圖目錄
圖(2.1) 預扭樑幾何座標圖…………………………..33
圖(4.1) 樑的等分圖……………………………………33
圖(5.1) 預扭角對於第一個自然頻率的影響………27
圖(5.2) 錐度比對於第一個自然頻率的影響………27
圖(5.3) 預扭角對於第二個自然頻率的影響………28
圖(5.4) 錐度比對於第二個自然頻率的影響………28
圖(5.5) 預扭角對於第三個自然頻率的影響………29
圖(5.6) 錐度比對於第三個自然頻率的影響………29
圖(5.7) 預扭角對於第四個自然頻率的影響………30
圖(5.8) 錐度比對於第四個自然頻率的影響………30
表目錄
表一 文獻比較…………………………………………24

參考文獻
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